Chatterjee coughs.
“When I asked Mr. Ramanujan about this scar, he told me that in India, before his departure for England, he underwent surgery for the treatment of a hydrocele. A swelling of the testicles. Is that correct, Mr. Ramanujan?”
Ramanujan waggles his head.
“Yet incredibly, none of the doctors who examined him took note of the scar, nor did he inform them that he had had such an operation.”
“I did not think it pertinent,” Ramanujan says.
“I therefore speculate,” Batty Shaw says, “that the operation was in fact not for the treatment of a hydrocele, but for the removal of a malignant growth on Mr. Ramanujan's right testicle. For whatever reason, the doctor chose not to inform Mr. Ramanujan of what he found. Subsequently the malignancy spread and now my theory is that Mr. Ramanujan is suffering from metastatic liver cancer.”
“Cancer?”
“It would explain all the symptoms, but most crucially the tenderness and enlargement of the liver.”
Hardy looks at Ramanujan. His face, as always these days, is without expression. And really, what extraordinary brutes doctors can be! They deliver the grimmest news without even a hint of compassion, as if the patient wasn't even in the room.
“The diagnosis would also be in keeping both with the nightly fevers and the low white blood count,” Batty Shaw says.
“But are you sure it's cancer? How can you be sure?”
Batty Shaw removes his tiny glasses. “Nothing is definitive,” he says, “though in my many years of experience, it has generally been the case that when the symptoms match a diagnosis, the diagnosis is correct.”
“So there's no way to tell for certain? No way to test?”
“Time will be the test.” He puts his spectacles back on. “If, as I surmise, Mr. Ramanujan has liver cancer, then within a very few weeks his condition will begin to deteriorate markedly.”
“Is there a treatment?”
“Neither treatment nor cure. He will live six months at most.” Almost as an afterthought, he adds: “I am very sorry.” The curious thing is, he says this to Hardy, not to Ramanujan. He doesn't even look at Ramanujan.
They get up to leave. Batty Shaw follows them through the door that leads into the corridor, Chatterjee with his arm around Rama-nujan's shoulder. And what is Chatterjee thinking? Has grief struck him dumb? Or is he raging, as Hardy is, not just at the arrogance, but the sloppiness of doctors? When the symptoms match a diagnosis, the diagnosis is correct… No student of mathematics would be allowed to get away with such fallacious logic! It seems to Hardy that doctors ought to have to prove their diagnoses, the way that mathematicians prove their theorems. Reductio ad absurdum. Let us postulate that indeed Ramanujan has liver cancer. Then …
“Sir.”
Hardy turns. Batty Shaw is beckoning him.
“I wonder if I might have a word with you in private.”
“Of course.”
Batty Shaw nudges closed the door to the waiting room, through which the Indians have already passed. “If you don't mind my asking,” he says, his voice low, “I was wondering about the bill …”
“What about it?”
“To whom should it be addressed?”
“To Mr. Ramanujan, of course.”
Batty Shaw raises his eyebrows. “But can he afford the expense?”
“All his medical bills are being paid out of his scholarship. Trinity can guarantee that.”
“I see.” Suddenly Batty Shaw looks impressed. “He told me nothing about himself, you see. What is he?”
“He is the greatest mathematician of the last hundred years. Possibly the last five hundred.”
“Really,” Batty Shaw says.
“Really,” Hardy says. And without another word, he passes through the door into the waiting room.
6
WHAT THOSE WHO have never experienced it firsthand do not know, Hardy is quickly learning. Illness is boring. For every brief episode of pain or despair, there are hours of inertia to be borne, during which fear quiets. Though fear is always present in the room of an invalid, you can't always hear it. But you feel it. A buzzing or trembling in your veins.
In the wake of Batty Shaw's diagnosis, there is nothing for Hardy and Ramanujan's other friends to do but brace themselves for the worst. Each day they wait for signs of deterioration to manifest themselves, however, and each day Ramanujan remains, so far as they can tell, exactly the same. His weight steadies, the nightly fevers keep to their schedule, the pain neither intensifies nor lessens. During the day he is lucid, if lethargic. Then at night the fevers come and he hallucinates. Ghosts appear before him, voices shout at him. Some nights he sees his own abdomen floating in the air above his bed. “Like a zeppelin?” Hardy asks, and he shakes his head.
“No, it takes the form more of a … a sort of mathematical appendage, with points attached to it that I have come to think of, or been told to think of, as ‘singularities.’ And what define these singularities are precise if mysterious mathematical surges. For example, when the pain is at its most steady and driving, I know that there is a surge at x = 1. And then I have to work to bring the pain down, and when it is half as intense, I know that the surge is now at x = —1. All night I work, trying to keep track of the surges, and to alleviate the pain by manipulating the singularities, so that by the time morning comes, and the fever has lifted, I am exhausted.”
“The Riemann hypothesis,” Hardy says. “The zeta function zooming off into infinity at 1.”
“Yes,” Ramanujan says. “Yes, I suppose that is part of it.”
“Perhaps,” Hardy suggests, “you may find the proof during one of your hallucinations.”
“Perhaps,” Ramanujan replies. But his voice is distant and disappointed, and he turns and looks out the window: for the moment, it appears, he is tired of talking.
They haul him back to Batty Shaw. Once again he is examined, once again Hardy (this time accompanied by Mahalanobis) is led by the nurse into the study with the swimming thing in formaldehyde and the model lung. “Well, you're right,” Batty Shaw says, wiping his tiny spectacles. “There appears to be no change in his condition.”
“Does that alter your diagnosis?”
“Perhaps. It may be too soon to tell. Cancer is not my specialty. We shall have to make an appointment for him to see Dr. Lees, the cancer specialist.”
And so, in due course, Ramanujan is taken to see Dr. Lees, the cancer specialist. By now his condition seems actually to have improved a little; that is to say, he manages the train journey more easily than he did the first time, and seems even to take some pleasure in being in London. Unfortunately, Dr. Lees proves to be even less helpful than Batty Shaw. While he agrees that Ramanujan's illness is not following the typical track of liver cancer, he can't say what track it is following. The liver remains enlarged and tender. His white blood cell count has increased only slightly. “A disease brought back from India?” he asks, and Hardy remembers the early proposition of an “Oriental germ.” This calls for yet another expert, Dr. Frobisher, specialist in tropical diseases. Unfortunately, so far as Dr. Frobisher can determine, Ramanujan's symptoms do not match the pathology of any known exotic malady. Swabs for malaria have come back negative. “Tuberculosis?” Dr. Frobisher asks, with hesitancy and humor in his voice, as if he is making a guess during a game of Charades. So they are back to tuberculosis! Oh, what a sloppy science is medicine!
It is decided that there is no good reason for Ramanujan to remain at the nursing hostel. From now on he will convalesce in his own rooms at Trinity. Hardy hopes this news will please him, but he greets it with typical indifference. Once again, he is put into his clothes; helped into a taxi. They drive the short distance to Trinity, where the porter awaits them. “Very good to see you again, sir,” he says, opening the taxi door and taking Ramanujan's case.
“I am glad to be home,” Ramanujan says, and Hardy is struck, even startled, that he should have come to think of Trinity
as home.
Then Hardy helps him through Great Court to Bishop's Hostel, and up the stairs to his rooms. The bedmaker appears to have cleaned them in his absence. The bed is tightly made. In the kitchen the dishes have been washed and stacked. She hasn't thrown out the rasam, though; it still sits in its pot, a thin veneer of mold on the top. Perhaps she was afraid to touch it.
Almost immediately upon entering the room Ramanujan starts to undress. This surprises Hardy, who always assumed him to be a modest man. Or perhaps the hospital stay was enough to abolish all modesty, for now he throws off his clothes with a recklessness to match Littlewood's. Hardy turns away—but only after catching a glimpse of Ramanujan's light brown body, the distended stomach sloping down toward the genitals, which are small and dark, deeply withdrawn between the legs. He cannot make out a scar in those shadows. And what a vulnerable thing, he thinks, is the male organ of procreation, especially when it is put before a doctor to squeeze or slice into! Most of the day it lies placid in its nest, a tiny, wretched thing, like a baby bird or a baby kangaroo. Then stimuli arouse it, it engorges with blood, doubles or trebles in size, and becomes the great thruster, the great, greedy, penetrating sword of pornography. Only to see it at rest, you would never believe it possible.
In any case, Ramanujan is naked just a few seconds. Soon he has pulled on his pyjamas, loosened the sheets, and climbed into the bed.
Who, now, is to care for him? Had this happened a year earlier, Hardy could have counted on the Nevilles to help. But now the Nevilles are in London, their house on Chesterton Road to let, so the responsibility falls to Hardy himself. The first week, Mahalanobis, Chatterjee, and Ananda Rao take it in turn to sit with the invalid, to inquire about his pain and to make sure he eats. Ananda Rao, to the best of his ability, prepares the meals. Unfortunately, this rotation proves tenable only until the term begins, at which point they are all far too busy, and Hardy must hire a nurse to look in on Ramanujan. Three times a week, she takes his temperature, monitors his stomach, listens to his chest and heart, then sends reports back to Dr. Wingate.
Ananda Rao continues to make Ramanujan's lunch and dinner. Mrs. Bixby takes charge of the sheets, which, due to the night sweats, have to be changed every morning.
For months he has hardly spoken about mathematics. At first this vexed Hardy; then he realized that he had no choice but to rein in his disappointment and focus his attention on work outside the purview of partitions. Since then he has written several papers on his own, and two with Littlewood, who, in his own way, is proving to be a less than reliable collaborator. For Littlewood, by his own account, is as depressed as Ramanujan. He despises his work at Woolwich. He longs to be in Treen with Mrs. Chase, and at the same time he cannot bear the thought of being in Treen with Mrs. Chase, because Mrs. Chase is raising her daughter to believe that Chase, not Littlewood, is her father. Whenever he and Hardy see each other in London, Littlewood wants to go to a pub. He drinks too much—beer and, less often, whisky. Nor is he willing to do much in the way of work on the papers they are writing together. “I leave the gas to you,” he tells Hardy—“gas” being their code word for the rhetorical flourishes, the elegantizing, that every good paper requires. Yet he is equally unwilling to do his share of the technical grunt work that every good paper requires just as much as it requires “gas.” Grunt work bores him, he says. Ballistics bores him. Too much boredom, and he will break down.
So it is for the time being. Of Hardy's two collaborators, one is ill, the other morose. Neither can be counted on.
As often as he can, he goes to see Ramanujan in the afternoons. He sits with him and tries to persuade him to eat, but just as at the nursing home Ramanujan complained that the cook did not prepare the dishes he required properly, now he complains that Ananda Rao's rasam is not to his taste. “It is not sour enough,” he says. “I'm sure he is using lemons instead of tamarind.”
“Even so, you must eat.”
“Did you know,” Ramanujan says suddenly, “that I made an important breakthrough in the partitions function while making rasam?”
“Did you now?”
“Yes. I was counting lentils. I started dividing them into groups.”
It seems an opening, if only a narrow one. “MacMahon and I continue our investigations, of course,” Hardy says. “He asked after you the other day.”
“Did he? How is he?”
“As well as any of us, under the circumstances. He sends you his best wishes.”
“That is kind of him.”
“Of course it goes much more slowly without you.”
“Yes, I am afraid I left off the work on partitions when I became ill. I apologize for that.”
“You need not apologize.”
“And what progress have you and the major made?”
Inadvertently Hardy smiles. Whatever hope he might be feeling right now he knows better than to indulge, as experience has taught him that hope cannot be relied on. And he is right: whatever curiosity he may have sparked in Ramanujan will dissipate within the hour. And yet, for the moment, the hope is real, and he grabs at it. The war has taught him to do this, to grab at what you can while it lasts. He tells Ramanujan what he has been thinking. Ramanujan waggles his head. Hardy takes a pen and some paper from his pocket, and for about half an hour, while Ananda Rao's inadequate rasam cools in its pot, they do what they have not done since spring. They work.
7
AT THE TIME, he did not take it very seriously. Or did he? He remembers the gales that day, the small boat docked at the pier in Esbjerg. Does he remember fear? No. It is curious— and perhaps something to be grateful for—that fear, like pain, doesn't last in memory. That is to say, though Hardy can remember, at various times, experiencing fear and pain, he cannot remember feeling fear and pain. Phrases such as “shortness of breath” or “constriction of the stomach” do not in and of themselves bring on shortness of breath or constriction of the stomach, perhaps because the very fact that you are now able to remember means that whatever provoked the fear or pain has been got past. Has been survived. The gales, the waves, the small boat rising and falling. Water splashing on the deck. The postbox nearby.
He was visiting Bohr in Copenhagen. Before the war, he often went to visit Bohr in Copenhagen. Bohr was younger than Hardy—in his mid-twenties—and had been on the Danish national football team when it placed second in the world in 1908. He wasn't exactly handsome: his brown hair, which he kept long, had a tendency to fly straight up, while the thick, downward slanting brows over his large eyes made Hardy think of the accent grave and the accent aigu in French. Still, there was something distinguished and memorable about his face. He had a lean, upright body. Like Littlewood, he was passionate about women, and noticed them, and took no notice of men.
The visits were always the same. Bohr would welcome Hardy at his apartment on the Stockholmsgade, then lead him straight through the sitting room and into the kitchen, where they would work out an agenda for the visit. The first item was always the same: “Prove the Riemann hypothesis.” Then they would take a walk along the moats and bridges of the Ostre Aenlag Park, even if it was winter, even if the trees were dusted with fine snow and the paths treacherous. Sometimes men and women would run up to Bohr and ask for his autograph, which he would provide with some embarrassment. For it wasn't the mathematician whose autograph they wanted; it was the football player's. It seemed that it was Bohr's fate always to come in second—later to his physicist brother, Niels; in those early days, to himself.
Once they got back to Bohr's kitchen, they would go to work. Usually they drank coffee. Sometimes they drank beer. It pleased Hardy to gaze across the table at Bohr as he scribbled on a pad, the stein of beer partially blocking his view of the thick hair sprouting from the top of his head.
Yet another brilliant man with hard legs who loved women.
Usually Hardy stayed three days. They never proved the Riemann hypothesis. Bohr always saw him to the station, where he caught the train t
o Esbjerg; walked to the dock and watched for the boat that was to carry him home. A small boat this time, rocking on big waves. Was it safe? The weather looked grim, a gray, thunderous sky and swooping winds. He sought out the captain and asked if it was safe, and the captain laughed, and pointed at the stormy sky as if it were nothing.
It was then that Hardy noticed the postbox. He thought of God. Later, he would tell himself that he did it only in order to have a good story to tell at Hall. And in fact he dined out on the story for years. Yet at the moment—he will admit it now—he felt real fear. He suffered shortness of breath, constriction of the stomach. He saw the boat capsizing, the passengers flailing in cold waters.
There was a little shop off the dock that sold picture postcards of Esbjerg. He bought a handful of them. He can't remember how many. And on each he wrote, “I have proven the Riemann hypothesis. G. H. Hardy.” And then he bought stamps, and carried them to the postbox, and dropped them in.
To whom did he send them? Littlewood, certainly—he remembers Littlewood ragging him about it later on. Possibly Russell. Certainly Bohr himself. And Gertrude. Or was it his mother? Or both? Perhaps he sent the postcard to his mother because he knew she would keep it, even if she didn't understand it. In any case, someone told the vicar.
For the idea, once again, was to outwit God. Were the ferry to sink, and Hardy to die, then the postcards would arrive after his death, and people would believe that he had proven the Riemann hypothesis, and that his proof had gone down with the ship, just as Riemann's proof had been fed to the flames. Hardy would then be remembered as the second man to have proven the Riemann hypothesis and lost his proof—and this God would not stand for. Or so Hardy believed. In order not to be bested by Hardy, God would make sure that he did not die. He would see the ship safely to its destination, and thereby insure that Hardy be denied any undue glory.
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